Rubber-blanket plates of the foregoing type are clamped onto rubber-covered blanket cylinders or transfer cylinders of rotary offset printing presses instead of conventional rubber blankets. As is known in the art, axial channels in the cylinder receive the ends of conventional rubber blankets or rubber-blanket plates which are clamped into fixed position. A disadvantage of known rubber-blanket plates is that edges of functional layers on the carrier plate (which typically is made of steel) are exposed to high mechanical loads and printing chemicals during high speed printing operations. This also occurs during washing of the blanket plates with conventional cleaning units. As a result, the individual functional layers of the blanket plate can become damaged or loosened from the carrier plate. Although it is known to seal the edges of the functional layers to the carrier plate, adhesion of the functional layers often is inadequate, or extensive stretching of the functional layers can result in the risk of stress cracks in the seal.